📘 Calculus I Course Overview

🎯 Course Description

Calculus I introduces students to the mathematics of change and accumulation, providing the foundation for advanced study in science, engineering, technology, and economics.

In this course, students will explore how quantities change, how to model real-world systems, and how to analyze those systems using powerful mathematical tools. Beginning with limits and continuity, the course builds toward derivatives, applications of derivatives, and integrals—culminating in the Fundamental Theorem of Calculus.

🚀 What You Will Learn

By the end of this course, students will be able to:

  • Evaluate and interpret limits

  • Determine continuity and apply the Intermediate Value Theorem

  • Compute and interpret derivatives using multiple methods

  • Apply derivatives to real-world problems such as:

    • Optimization

    • Related rates

    • Linear approximation

  • Understand and compute antiderivatives

  • Evaluate definite integrals and interpret them as accumulation

  • Apply the Fundamental Theorem of Calculus

  • Use substitution to simplify and solve complex integrals

🧠 How You Will Learn

This course is designed to support deep understanding through multiple learning approaches:

  • 📊 Interactive Visualizations (Desmos activities)

  • 🎥 Instructional Videos

  • 📝 Structured Practice Worksheets

  • 🎮 Engagement Activities (Kahoot, Jeopardy-style games)

  • 👥 Collaborative Learning & Guided Support

  • 🧠 Concept-Based Assessments

Students will not only learn how to perform calculations, but also how to interpret, explain, and apply calculus concepts.

🔗 Course Structure

The course is organized into the following major units:

  1. Limits & Continuity

  2. Derivatives & Rules

  3. Applications of Derivatives

  4. Antiderivatives

  5. Definite Integrals

  6. Fundamental Theorem of Calculus

  7. Substitution (u-Substitution)

Each unit builds on the previous one, creating a cohesive understanding of calculus as a complete system.

🌍 Real-World Connections

Calculus is used to model and solve problems involving:

  • Motion and velocity

  • Growth and decay

  • Optimization of resources

  • Engineering and design

  • Economics and data analysis

Throughout the course, students will connect mathematical concepts to real-world scenarios and applications.

🎓 Who This Course Is For

This course is ideal for students who:

  • Are preparing for STEM majors or careers

  • Want to strengthen problem-solving and analytical thinking

  • Are interested in understanding how mathematics describes the world

💡 Course Philosophy

This course emphasizes:

👉 Understanding over memorization
👉 Strategy over shortcuts
👉 Application over isolation

Students will develop the ability to not only solve problems, but also to explain their reasoning and apply their knowledge in new situations.

🔥 Final Outcome

By the end of this course, students will have built a complete understanding of:

👉How things change(derivatives)
👉How things accumulate(integrals)
👉How those ideas are connected(Fundamental Theorem of Calculus)